Drip machines and percolators take up too much space, French presses are a hassle to clean, and instant machines make coffee that tastes like crap. How to quickly make a cup of Joe that tastes great and leaves little mess? There are a number of options. The kitcheneers at Stack Exchange give you a few of them.

Lifehacker Answer: AeroPress

Normally we leave all these answers to the users from Stack Overflow, but since I've got a strong opinion on this one, I'll add my two cents. You'll see this mentioned below as well, but for $25 on Amazon, the AeroPress makes some of the best coffee you'll ever taste, and it's incredibly easy to clean up. You can brew coffee with an AeroPress in many different ways, but I've had my best cups using Ben's method from the World AeroPress Championships recipe page.

As a final note, freshly roasted, whole beans make a huge difference, and a burr grinder will serve you better than a blade grinder. Since you're not looking at spending much, a crank burr grinder is probably your best bet.

Answer: La Macchinetta & La Macchinetta Napoletana

These are ubiquitous in Italy, where it is called la macchinetta - the little machine. Every household has one, or often more then one, with different sizes. The classical one is sold by Bialetti.

Use is simple: fill with water, fill with coffee, throw on the stove, wait, and pour. Maintenance is easy. With a Moka, soaping and overwashing are discouraged.

Also used in Italy: the macchinetta napoletana, known in the States as the flip-over coffee pot. See Eduardo de Filippo, one of the best Italian actors of all time, speak of the macchinetta napoletana's virtues (in Italian) in this scene from Questi fantasmi.

Answer: The Cezve (AKA the Ibrik)

A cezve is an easily cleanable pot that allows you to make Turkish coffee. In my opinion, the cezve is the way to go when it comes to making coffee quick and easy and with minimal clean up. Check out these instructions on how to use a cezve (sometimes called an ibrik).

Answer: AeroPress

I use an AeroPress. Its cheap, quick (if your water's hot, it can take less than a minute), super easy to keep clean and it makes high-quality (and versatile) coffee.

It requires a small filter (I bought a pack of 250 or so when I first got it 18 months ago and I'm only just running out now). The finished grounds are pressed into a "puck" which makes for convenient and dry trashing. See this video tutorial to learn how to use an AeroPress.